Mechanical arms play a pivotal role across various domains, yielding significant improvements in automation, precision, efficiency, and safety. For a single-link mechanical arm dealing with unknown loads and constrained control inputs, the rotational inertia J is often unknown and can not be directly designed into control laws. To address this, this study employs adaptive estimation for rotational inertia and designs mapping adaptive laws. As a result, achieving control within limited inputs becomes feasible, with the extent of input limitations adjustable via parameters. Through Lyapunov analysis, the system’s convergence to a compact set of small radius is proven, and the efficacy of the proposed control approach is verified through MATLAB/SIMULINK numerical simulations.